Adaptive parameter estimation for degenerate parabolic systems
type: Item
instance of: scholarly article
title: Adaptive parameter estimation for degenerate parabolic systems
zbMATH Open document ID: 0827.93032
author: I. G. Rosen
author: Michael A. Demetriou
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-12-11T00:00:00Z
review text: Parameter identification, or estimation, simply means the determination of unknown parameters (which may be either scalar, vector, or functional) in a proposed model for a given physical system based upon input/output data. Here, an adaptive (on-line) identification scheme for first-order in time implicit and possibly degenerate distributed parameter systems is considered. A state and parameter estimator are defined as the coupled states of an initial value problem for an infinite-dimensional non- degenerate evolution equation. The aim of the article is to establish that the state and parameter estimators asymptotically approach the true values of the corresponding parameters and the corresponding plant state. For the state convergence a Lyapunov -- like argument is used, while for the parameter convergence an additional assumption known as ``persistence of excitation'' is required. An example concerning the identification of a degenerate one-dimensional heat equation is discussed and some numerical results are provided.
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 765101
zbMATH Keywords: implicit possibly degenerate parabolic system
zbMATH Keywords: adaptive scheme
zbMATH Keywords: parameter identification
zbMATH Keywords: heat equation
reviewed by: Zdzisław Denkowski
MaRDI profile type: Publication
OpenAlex ID: W2078999924
DOI: 10.1006/JMAA.1995.1053
description: scientific article; zbMATH DE number 765101